# Ionic mobilities and conductivities of lithium and potassium cations in acetonitrile–propylene carbonate solution

Recently I calculated the ionic mobility and molar ionic conductivity values for $$\ce{Li+}$$ and $$\ce{K+}$$ cations in an acetonitrile–propylene carbonate binary mix solution (8:2 molar fraction ratio).

For AN–PC 8:2, $$T = \pu{273 K},$$ dynamic viscosity of the binary AN–PC solution $$η = \pu{0.737*10^3 Pa s}$$ I calculated the values for ionic mobility

$$μ = \frac{ez}{6πηa}\quad(\pu{m^2 V^-1 s^-1})\tag{1}$$

and molar ionic conductivity

$$λ = zμF\quad(\pu{S m^2 mol^-1}).\tag{2}$$

According to this the mobility of $$\ce{K+}$$ is 5 times higher than that of $$\ce{Li+}$$, and the molar ionic conductivity of $$\ce{K+}$$ is 27 times higher than that of $$\ce{Li+}.$$

Is it correct to calculate with these formulas?

• $\eta$ is unitless magic number or dynamic viscosity with a unit ? It seems rather big. How did you get $a$ ? Does it consider solvation ? How have you got 5 and 27 multiples ? They should be the same. Jul 15 '21 at 12:50
• I used the ionic radius of K and Li: 1.45 Å and 0.92 Å respectively. (Johnson, O. (1973). Ionic Radii for Spherical Potential Ions. I. Inorganic Chemistry, 12(4), 780–785) Jul 15 '21 at 13:31
• Remember that in water, hydrated lithium ion is bigger than potassium one, with lower mobility and molar conductivity, even if a naked lithium ion is smaller than a naked potassium ion. It guess it will be similar for other polar solvents. By other words, you cannot use ion radius, unless it is explicitly stated it is the (effective) hydrated ion radius. Jul 15 '21 at 13:36
• The problem is that in context of ion mobility in solvents, the efficient ion radius is calculated from the actual ion mobility and not vice versa. As the effective ion radius is scenario dependent. Jul 15 '21 at 14:34
• Thanks for the clarification. So after all, we could say, that K+ ions have higher molar ionic conductivity therefore mobility (lower hydrated ionic radius) in water regardless of the accompanied anion it has (e.g. LiTFSi vs KTFSi, or LiCl vs KCl)? According the Kohlrausch's law, this is what I conclude. Is it right? How to interpret this law for other electrolyte solutions: acetonitrile or propylene carbonate for example? Jul 16 '21 at 13:25